Universal Polar Instability In Highly Orthorhombic Perovskites

The design of novel multiferroic ABO$_3$ perovskites is complicated by the presence of necessary magnetic cations and ubiquitous antiferrodistortive modes, both of which suppress polar distortions. Using first-principles simulations, we observe that the existence of quadlinear and trilinear invariants in the free energy, coupling tilts and antipolar motions of the A and B sites to the polar mode, drives an avalanche-like transition to a non-centrosymmetric $Pna2_1$ symmetry in a wide range of magnetic perovskites with small tolerance factors - overcoming the above restrictions. We find that the $Pna2_1$ phase is especially favoured with tensile epitaxial strain, leading to an unexpected but technologically useful out-of-plane polarization. We use this mechanism to predict various novel multiferroics displaying interesting magnetoelectric properties with small polarization switching barriers.